The Aviation Herald reports that in an incident that took place on 26th July but that has only come to light in the last few days, an Airbus A340 doing a FRA-MAD route performed an emergency landing in Valencia after it could not land in Madrid due to thunderstorms.
3 Ryanair 738s also performed mayday landings, though
only one of them actually landed below the 30 min reserves, but only
marginally. These have been discussed elsewhere, and have been widely reported, whereas the LAN
340 had been kept quiet despite what appears to be a more critical situation.

According to the report, the A340 lost an engine during the approach to VLC, where it landed substancially below the minimum reserves.

Although the report does not state that the engine loss was the result of low fuel, it would seem too much of a coincidence if these were not related.

It would be useful to hear the views of professionals, as to what could have happened here. Is 800 kg in one wing tank low enough to cause starvation in one engine? Might this have been a deliberate shut down to save fuel?
Are engines fed from different tanks, and so engine loss can be staggered in a low fuel situation?

I´m not exactly sure if the engine failure could be atrributed to the low fuel state. Usually, when the engines start failing due to fuel starvation, they will all fail within a very few minutes. Then again, I´m no expert on the fuel systemof the A340.

Has an actual investigation been launched by the Spanish authorities? That would surely happen if the failed engine was due to low fuel.

Para 2.5, states that if the crew believes that they will land with less than final reserve fuel then a Fuel emergency (Mayday) is to be made. If two a/c landed with more than final reserve may indicate that ATC got them on the ground with priority. As would be expected!!

As I had heard the LAN Chile on 3 engines into VLC placed further problems onto ATC, which placed a 30 minute delay on diverted aircraft from MAD. Not a good night.

Actually, it was not the 737s that had that amount of fuel. The 737 that landed just below the minimum reserve had 1029 Kg -which would according to the Aviation Herald is 75 Kg less than required and so just short of half an hour's flying time.

The same report says that the Lan Chile A340 consumed 700 Kg of the reserve!, leaving just 800 Kg in one wing and 1300 Kg in the other.

Quoting AR385 (Reply 1):Has an actual investigation been launched by the Spanish authorities? That would surely happen if the failed engine was due to low fuel.

The Herald says that when they enquired with the spanish authorities did not intend to launch an investigation on any of the emergency landings at VLC on 26th July.
I have since heard the minister with responsibility for the aviation safety agency in Spain say in response to media pressure on the Ryanair cases that those will be investigated, and that they would not be shy to impose sanctions.
However, neither the media nor the authorities seem interested in the LAN Airbus A340, which seems a more critical case.

From my non-professional point of view, but based on what I have read is that in the cases of the Ryanair 737s, I don't see how they can be accused of not loading enough fuel. But should at least one of them have started the deviation to VLC before they had spent 27 minutes circling around MAD?